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Abstract

Fast and accurate geometric characterization and metrology of noble metal nanoparticles such as gold nanorod (NR) ensembles is highly demanded in practical production, trade, and application of nanoparticles. Traditional imaging methods such as transmission electron microscopy (TEM) need to measure a sufficiently large number of nanoparticles individually in order to characterize a nanoparticle ensemble statistically, which are time-consuming and costly, though accurate enough. In this work, we present the use of optical extinction spectroscopy (OES) to fast measure the aspect ratio distribution (which is a critical geometric parameter) of gold NR ensembles statistically. By comparing with the TEM results experimentally, it is shown that the mean aspect ratio obtained by the OES method coincides with that of the TEM method well if the other NR structural parameters are reasonably pre-determined, while the OES method is much faster and of more statistical significance. Furthermore, the influences of these NR structural parameters on the measurement results are thoroughly analyzed and the possible measures to improve the accuracy of solving the ill-posed inverse scattering problem are discussed. By using the OES method, it is also possible to determine the mass-volume concentration of NRs, which is helpful for improving the solution of the inverse scattering problem while is unable to be obtained by the TEM method.

Fig. 3 Comparison of the measured AR distribution functions of three gold NR ensemble samples obtained by the OES method (red) and those obtained by the TEM method (black). In each subfigure, both the discrete AR distribution and a Gaussian fit of it are given. The values in parentheses (
AR¯, σAR) give the mean AR and the standard deviation of the PDF obtained by the two methods.

Fig. 4 (a) Comparison of the retrieved ARD p(AR) obtained by the OES method using different assumed mean width D̄ and the p(AR) directly measured by the TEM method. (b) Dependence of the mean square error mse on the assumed mean width D̄.

Fig. 5 (a) Dependence of the retrieved mean aspect ratio
AR¯ and the standard deviation σ on the assumed mean width D̄ for sample NR-20-700 with assumed ē = 0.6. (b)Dependence of the number of NRs per unit volume Nv and the mass-volume concentration Cg of NRs on the assumed mean width D̄.

Fig. 6 (a) Comparison of the retrieved ARD p(AR) obtained by the OES method using different assumed mean end-cap eccentricity ē and the measured p(AR) obtained by the TEM method. (b) Dependence of the mse on the assumed ē.

Fig. 8 Comparison of the retrieved p(AR) obtained by the OES method by assuming (a) different polydispersities of the width D and a fixed e = 0.6, and (b) different polydispersities of the end-cap eccentricity e and a fixed D = 20 nm.